To square root the Lagrangian or not: an underlying geometrical analysis on classical and relativistic mechanical models
| Autor: | Rizzuti, B. F., Júnior, G. F. Vasconcelos, Resende, M. A. |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The geodesic has a fundamental role in physics and in mathematics: roughly speaking, it represents the curve that minimizes the arc length between two points on a manifold. We analyze a basic but misinterpreted difference between the Lagrangian that gives the arc length of a curve and the one that describes the motion of a free particle in curved space. Although they provide the same formal equations of motion, they are not equivalent. We explore this difference from a geometrical point of view, where we observe that the non-equivalence is nothing more than a matter of symmetry. As applications, some distinct models are studied. In particular, we explore the standard free relativistic particle, a couple of spinning particle models and also the forceless mechanics formulated by Hertz. Comment: 19 pages, no figures, geometrical perspective in reparametrization invariance and forceless mechanics of Hertz. Some formulae were corrected from the previous v1 version |
| Databáze: | arXiv |
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